David's blog post says that:
Thus, any text tagged with <H1> is assigned to the Titles field and placed at the top level of the browser hierarchy, just as if you had placed the red T in the margin of the tool's Edit window. Accordingly, <H2> is placed at the second level of the browser hierarchy (as if you had placed a red "1" in the margin of the Edit window); <H2> is placed at the third level of the browser hierarchy (as if you had placed a red "2" in the margin); etc.
This hasn't been my experience. I have a dummy document has a five separate <H1> tags; only one heading appears in the browser at top level. Instead, everything is buried further and further down the hierarchy, to the point where a <h3> tag (say, around "Book Third") is buried seven levels down.
It seems like something isn't resetting a counter properly, as all new higher-level sections are being interpreted as subsections of previous ones.
(Since I can't upload a HTML file via the forums, if you want to try and replicate this, you can get the sample document here.)